Note that reported suicide rates are extremely vulnerable to reporting bias, arising from both unintentional and deliberate misclassification of deaths.

A variety of social, culture, religious, economic, political, and criminal factors affect the detection of deaths by suicide and how they are reported. (He accidentally took too many pain pills. She accidentally blew her head off while cleaning her gun collection.)

Heck, just being in a country that conducts more autopsies is associated fairly strongly with a higher reported suicide rate. This 2011 study in JAMA Psych found that a 1% increase in autopsy rate was associated with a 0.45 per 100,000 increase in suicide rate.